powerseriesexpansionanditsapplications-外文文獻(xiàn)(已修改)
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【正文】 209NO .8O O OPrincipleofmathematicalnalysi208PowerSerisExpansionadItsAplicationsLiangHui(梁惠 )（MajorinPureandAppliedMathem atics053,HangzhouTeacther’sCollage,310000）AbstractBylearnigsom ebasicknowledgeofpowerseris,and m nelm eywordsK K K Powerseris； Maclurin(Maclurin)form ula； Taylorform ula,； Elem ntaryfunctionPowerserisiaveryim portantcontetofm athem atical anlysi,andpowerserishasverywiderangeofaplications,canusethepowerserisexpansion,it39。seasytoslvesom eofthem ore plexproblem s,thepuroseofthispaeristoresarchtepowerserisexpansionandtheaplicationofelm (Maclurin)form ulaPolynom ialpowerseriscanbesenasnextnsionfreality,sosiderthefunction()fxcanexpandintopwerseris,youcanfrom thefunction()fxandpolynom ialsstartoslvethisproblem .Tothisend,togivehrewithoutprofthefolwingform (Taylor)form ula,ifthefunction()fxat 0xx=inaneighborhodthatuntilthederivativeofrder1n+,thenithenighborhodfthefolwingform ula:20 0 0 0()()( )( ) ( )()nnfxfxxxxx xxrx=+?+?++?+… (951)Am ong 10()( )nnrxxx+=?That()nrxf
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